Redirect after empty login username and password

I have chosen to display a login form in the first page of my wordpress website. If the user logs in successfully, he gets redirected to a specific webpage. If he enters a wrong password, he gets redirected to the login page again. The problem happens when someone does not enter username and password: he gets redirected to the wordpress admin login page.

How can I redirect empty username logins back to the main login page ?

this is the code I am using to redirect failed attempts :

add_filter('login_redirect', '_catch_login_error', 10, 3);

function _catch_login_error($redir1, $redir2, $wperr_user)
{
    if(!is_wp_error($wperr_user) || !$wperr_user->get_error_code()) return $redir1;

    switch($wperr_user->get_error_code())
    {
        case 'incorrect_password':
        case 'empty_password':
        case 'invalid_username':
        default:
            wp_redirect(home_url()); // modify this as you wish
    }

    return $redir1;
}